An electrochemical system is a system that either derives electrical energy from chemical reactions, or facilitates chemical reactions through the introduction of electrical energy. An electrochemical system generally includes a cathode, an anode, and an electrolyte, and is typically complex with multiple heterogeneous subsystems, multiple scales from nanometers to meters. Examples of these systems include fuel cells, batteries, and electroplating systems. On-line characterization of batteries or fuel cells in vehicles is difficult, due to very rough noisy environments.
On-line characterization of such electrochemical systems is desirable in many applications, which include real-time evaluation of in-flight batteries on a satellite or aviation vehicle, and dynamic diagnostics of traction batteries for electric and hybrid-electric vehicles. In many battery-powered systems, the efficiency of batteries can be greatly enhanced by intelligent management of the electrochemical energy storage system. Management is only possible with proper diagnosis of the battery states.
Batteries have attracted great interest for automotive and in-flight applications, such as unmanned aerial vehicles, due to the potential for high energy and power density, wide temperature range, and long cycle life. In order to realize the full benefit of traction batteries, efficient energy management is essential. These applications require a battery-state estimator to ensure accurate and timely estimation of the state of charge, the charge and the discharge power capabilities, and the state of health of the battery. The open-circuit voltage (OCV) is a pivotal parameter for all of these estimates.
The open-circuit voltage is a thermodynamic parameter; OCV is therefore usually measured when the battery is in thermodynamically reversible equilibrium. However, in most on-line applications of a battery, it is desirable to estimate OCV in situ.
Although there may be many kinds of characterization models for batteries, equivalent circuit models are appropriate in many applications where stringent real-time requirements and limiting computing powers need to be considered. An algorithm for a circuit model is relatively simple, meaning that simulation time is short and the computation cost is relatively low. A circuit model is an empirical model that describes the electrochemical system with, for example, a resistor-capacitor or resistor-inductor-capacitor circuit.
In a suitable circuit model, major effects of thermodynamic and kinetic processes in the battery can be represented by circuit elements. For example, the electrode potential between the cathode and the anode of a system can be represented with a voltage source, the charge-transfer processes can be represented with charge-transfer resistances, the double-layer adsorption can be represented with capacitances, and mass-transfer or diffusion effects can be represented with resistances such as Warburg resistances. A circuit model can be useful for many on-line diagnostics of the real-time states of an electrochemical system.
However, it can be difficult to accommodate non-linear diffusion processes in circuit models. Diffusion can be the major limiting step of the overall kinetics within a battery. In most Li-ion battery-powered applications, mass-transfer effects are the main factor in limiting the rate of kinetic processes inside the battery. It is extremely difficult, if not impossible, to represent diffusion phenomena with conventional resistor and capacitor elements. It has been attempted to use non-linear devices to describe the diffusion, but results have not been satisfactory.
There are several types of algorithms for a circuit model. These algorithms include parametric regression of circuit analog, Kalman filter, fuzzy logic, pattern recognition, and impedance spectroscopy. Fuzzy logic and pattern recognition are not reliable and practical because they are less relevant to a physical description of the system. Impedance spectroscopy is a relatively mature algorithm and is extensively used in lab equipment, but is less useful for on-line real-time characterization because it needs relatively long time (on the order of minutes).
Prior methods include those described in Xiao et al., “A universal state-of-charge algorithm for batteries,” 47th IEEE Design Automation Conference, Anaheim, Calif., 2010. This paper deduces the impulse response for state-of-charge estimation of batteries. The model is a superposition of a constant voltage source and a linear circuit box characterized by an impulse-response function. That is, Xiao et al. assume that the open-circuit voltage is constant within the sampling period. This requirement may be too stringent for most applications involving batteries as the power sources. In addition, the algorithm does not acknowledge signal noise, and therefore may be limited in on-line applications.
Other prior methods include those described in U.S. Pat. No. 7,015,701, issued to Wiegand and Sackman; U.S. Pat. No. 6,339,334, issued to Park and Yoo; U.S. Pat. No. 7,504,835, issued to Byington et al.; and U.S. Pat. No. 5,633,801, issued to Bottman. These patents describe methods to measure electrochemical impedance in the time domain. These patents disclose different time signals for exciting the detected electrochemical systems. Wiegand and Sackman disclose frequency-rich alternating current signals, Park and Yoo disclose differential delta functions, Byington et al. disclose broadband alternating current signals, and Bottman discloses short pulse signals. These patents do not disclose techniques to address data noise and other real-time, on-line challenges.
A physics-based electrochemical model may be able to capture the temporally evolved and spatially distributed behavior of the essential states of a battery. Such analyses are built upon fundamental laws of transport, kinetics and thermodynamics, and require inputs of many physical parameters. Because of their complexity, longer simulation times are needed, and there is no assurance of convergence in terms of state estimation. Thus, while these more complex models are suitable for battery design and analysis, they have not been used in commercial battery state estimators.
Due to limited memory storage and computing speed of embedded controllers employed in many applications and the need for fast regression in terms of parameter extraction, a zero-dimensional lumped-parameter approach based on an equivalent circuit model (parametric circuit model) has been found to be most practical for battery-state estimation. A circuit employing a resistor in series with a circuit element comprising a parallel resistor and capacitor has been employed successfully for embedded controllers.
In view of the shortcomings in the art, improved algorithms for characterizing batteries (and other electrochemical systems) are needed. These algorithms, and the apparatus and systems to implement them, preferably are able to broadly accept various exciting signals, are stable and robust against noises, and are agile for real-time use, even when diffusion is a limiting kinetic factor in the battery.
In practical applications, noise must be addressed in order to deduce an impulse response through one or more noise-reduction techniques. The impulse response should enable calculation of battery open-circuit voltage, and in turn, various states of the battery. Preferably, algorithms should not require a constant open-circuit voltage within a sampling period, but rather, only that its rate of change be smaller than the rate of change of the measured electrode potential, since this constraint is satisfied in most of real applications. The calculations should be executable in the time domain so that it is feasible for on-line implementation.